# How Many Types of Polish Notation Are There in Data Structure?

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Heather Bennett

How Many Types of Polish Notation Are There in Data Structure?

Polish notation, also known as prefix notation, is a way of writing arithmetic expressions without using parentheses to indicate the order of operations. In this article, we will explore the different types of Polish notation used in data structures and their significance.

## 1. Polish Notation (PN)

The standard form of Polish notation is known as PN or 0-ary Polish notation. In this form, operators are written before their operands. For example:

```+ 5 3
```

This expression represents the addition of 5 and 3. The operator ‘+’ comes before its operands, ‘5’ and ‘3’.

## 2. Infix Notation

In contrast to Polish notation, infix notation is the most common way of writing arithmetic expressions. In infix notation, operators are placed between their operands. For example:

```5 + 3
```

This expression represents the same addition as the previous example but in infix notation.

## 3. Reverse Polish Notation (RPN)

Reverse Polish Notation (RPN), also known as postfix notation, is another type of Polish notation where operators are placed after their operands.

```5 3 +
```

This expression represents the same addition as the previous examples but in RPN.

## 4. Extended Reverse Polish Notation (ERPN)

In some cases, an extended version of RPN called Extended Reverse Polish Notation (ERPN) is used.

ERPN allows for multiple operators to be written after their respective operands.

```5 3 + *
```

This expression represents the multiplication of the sum of 5 and 3. The operator ‘+’ is evaluated first, followed by the operator ‘*’.

## 5. Polish Notation with Function Symbols

In addition to arithmetic expressions, Polish notation can also be extended to include function symbols.

```sin 45
```

This expression represents the sine function applied to an angle of 45 degrees.

### Conclusion

Polish notation is a unique way of writing arithmetic expressions that eliminates the need for parentheses. There are different types of Polish notation, including PN, infix notation, RPN, ERPN, and even Polish notation with function symbols. Each type has its own significance and use cases in data structures and algorithms.

To summarize:

• Polish Notation (PN): Operators before operands.
• Infix Notation: Operators between operands (commonly used).
• Reverse Polish Notation (RPN): Operators after operands.
• Extended Reverse Polish Notation (ERPN): Multiple operators after operands.
• Polish Notation with Function Symbols: Including function symbols in expressions.

Understanding these different types of Polish notation can enhance your understanding of data structures and algorithms and broaden your programming skills.